The Blues signed Michel from Sporting Gijon and Craig Gardner from Aston Villa in the January transfer window.
McLeish will be backed by the finances of new owner Carson Yeung.
Dunford said: “I expect it to be quite a busy summer. We will gear ourselves up for what I’m sure will be significant transfer movement in the summer.
“There are also eight or nine players likely to be leaving the club which means from a numerical point of view, we need new players of quality to supplement the ones we have got as well.”
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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